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C22×#91242 #14412048

order1920
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC22×#91242

Splittings

HallC3×C5 ⋊ C22×#100
SylowC5 ⋊ C22×#833
SylowC3 ⋊ C22×#4013

Subgroups

subgroupG/H
centerC23#6763
commutatorC22×C3×C5C23×C4
FrattiniC22C23×ΓL(1,𝔽16)
FittingC25×C3×C5C4
socleC23×C3×C5C22⋊C4
prime radicalC23×C3×C22⋊D5C2
cosocleC2×C3×Dic5C24
hypercenterC25ΓL(1,𝔽16)
hypocenterC3×C5C22×#100
LCSG ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C24 ◁ C25

1984 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

180 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 137746);